The evolution from local toward virtualized data storage, computing, applications and services – in the forms of Internet of Things (IoT), Everything as a Service (EaaS), and Cloud computing – has changed the way of delivering digital services for consumers and businesses. These technologies have brought clear benefits over traditional systems, such as easy management, universal availability, and decreased hardware requirements for end-user devices. The main challenges of the first-generation IoT services are related to communication latency due to high physical and logical distance between end nodes and server resources and vulnerability for network problems along the long routes. Thanks to the unveiling of the fifth-generation wireless technology (5G) for cellular networks, the last-mile connection performance – communication latency in particular – is taking a huge leap and therefore introducing new possibilities for industrial applications. Edge computing is a key technology to unleash the full potential of the arising industrial wireless communication, since it enables deploying computational tasks to computing nodes near the end devices and therefore opens novel business opportunities around real-time cloud services. In this chapter, we introduce the current state of the art and discuss different challenges the edge computing systems are facing particularly in the Industrial IoT (IIoT) domain, as well as present potential solutions for the identified challenges.